Nonlocal regularization and the one-loop topological mass in three-dimensional QED

We reexamine the regularization of the one-loop gauge-boson self-energy in three-dimensional QED with no topological mass at the tree level. Because this theory is finite, there can only be one value for the quantum correction to the gauge-boson mass. Using the recently developed technique of nonlocal regularization, we find that the gauge boson acquires a nonzero topological mass at one loop, a result consistent with dimensional, analytic, and operator regularization, but not with the method of Pauli and Villars